Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs

Transcription

1 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs SIMONE BRIENZA, University of Pisa MANUEL ROVERI, Politecnico di Milano DOMENICO DE GUGLIELMO and GIUSEPPE ANASTASI, University of Pisa Recent studies have shown that the IEEE MAC protocol suffers from severe limitations, in terms of reliability and energy efficiency, when the CSMA/CA parameter setting is not appropriate. However, selecting the optimal setting that guarantees the application reliability requirements, with minimum energy consumption, is not a trivial task in wireless sensor networks, especially when the operating conditions change over time. In this paper we propose a Just-in-Time LEarning-based Adaptive Parameter tuning (JIT- LEAP) algorithm that adapts the CSMA/CA parameter setting to the time-varying operating conditions by also exploiting the past history to find the most appropriate setting for the current conditions. Following the approach of active adaptive algorithms, the adaptation mechanism of JIT-LEAP is triggered by a change detection test only when needed (i.e., in response to a change in the operating conditions). Simulation results show that the proposed algorithm outperforms other similar algorithms, both in stationary and dynamic scenarios. CCS Concepts: Networks Network Protocols Additional Key Words and Phrases: Wireless sensor networks, IEEE , CSMA/CA, active adaptive algorithms, change detection tests ACM Reference Format: Simone Brienza, Manuel Roveri, Domenico De Guglielmo, and Giuseppe Anastasi Just-in-time adaptive algorithm for optimal parameter setting in WSNs. ACM Trans. Autonom. Adapt. Syst. 10, 4, Article 27 (January 2016), 26 pages. DOI: 1. INTRODUCTION Wireless sensor networks (WSNs) are composed of a large number of tiny sensor nodes deployed over a certain geographical area and interconnected through wireless links. Each node is a low-power device that senses physical information from the surrounding environment, performs local processing of acquired data, and transmits that data to a coordinator node referred to as a sink. Given the relatively low-cost, simple installation and ease of deployment, WSNs are increasingly perceived as an effective technology for developing distributed sensing systems in a large number of application domains, ranging from environmental monitoring to logistics, from health care to industrial applications, from building automation to smart cities. This positive trend is also pushed 27 This work was partially supported by the University of Pisa, in the framework of the PRA 2015 program. Authors addresses: S. Brienza, D. De Guglielmo, and G. Anastasi, Department of Information Engineering, University of Pisa, Largo Lazzarino 1, 56122, Pisa, Italy; s: simone.brienza@for.unipi.it, d.deguglielmo@iet.unipi.it, giuseppe.anastasi@unipi.it; M. Roveri, Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy; manuel.roveri@polimi.it. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY USA, fax +1 (212) , or permissions@acm.org. c 2016 ACM /2016/01-ART27 $15.00 DOI:

2 27:2 S. Brienza et al. by a number of available communication standards for WSNs [IEEE 2006; ZigBee 2007; HART 2012; ISA 2009]. Among them, IEEE [IEEE 2006] is certainly the most popular one for commercially available, off-the-shelf sensor platforms. A proper choice of communication protocol is of fundamental importance in WSNs, since sensor nodes are energy constrained and communication is typically the most energy-consuming activity [Anastasi et al. 2009]. In this perspective, IEEE is a standard specifically designed for low-power, low-rate, low-cost Personal Area Networks (PANs) that defines the physical (PHY) and Medium Access Control (MAC) layers of the protocol stack. It supports both star and peer-to-peer topologies, and provides two different operation modes: Beacon Enabled (BE) and Non-Beacon Enabled (NBE). In this article, we focus on the BE mode, since it is the most popular one, and provides a power-saving mechanism, based on duty cycling. In BE mode, nodes periodically wait for the reception of a special control message, called a Beacon, from the coordinator node. Then, they transmit their data packets using a slotted Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) algorithm to access the shared wireless medium. As mentioned earlier, energy efficiency is typically the most critical aspect to consider in the design of WSN-based systems. However, in many application domains, additional requirements, such as reliability and timeliness, must be taken into account [Zurawski 2009]. In this respect, several studies [Yedavalli and Krishnamachari 2008; Singh et al. 2008; Pollin et al. 2008; Anastasi et al. 2011] have highlighted that WSNs suffer from severe limitations in terms of reliability (i.e., low packet delivery probability) and timeliness (i.e., high packet latency). These limitations are mainly due to the CSMA/CA algorithm used by the MAC protocol. As is well known, the packet delivery probability of CSMA/CA protocols degrades sharply when the number of nodes increases. In the MAC, this degradation is even stronger than in other similar MAC protocols due to the default CSMA/CA parameter values suggested by the standard. Anastasi et al. [2011] have shown that these default values are not appropriate, even when the number of sensor nodes is low. The delivery probability can be increased by using higher CSMA/CA parameter values. However, this comes at the cost of a higher latency and energy consumption. Hence, an appropriate parameter setting should be found, depending on the application requirements. Ideally, the CSMA/CA parameter setting should be chosen to guarantee the reliability (and timeliness) requirements of the application with minimum energy consumption at sensor nodes. However, in real WSNs, the identification of such an optimal setting is not a trivial task, as reliability and timeliness strongly depend on a number of time-varying factors such as number of sensor nodes, offered load, and packet error rate (PER) that can neither be controlled nor predicted. Several solutions have been proposed to identify the optimal CSMA/CA setting in WSNs. They can be broadly classified as model-based strategies [Park et al. 2009; Park et al. 2013], and measurement-based strategies [DiFrancesco et al. 2011; Brienza et al. 2013a]. A detailed analysis of the related literature is presented in Section 2, in which we also emphasize the limitations of the existing solutions. To overcome these limitations, in this article, we propose a Just-in-Time LEarningbased Adaptive Parameter tuning (JIT-LEAP) algorithm. JIT-LEAP follows a measurement-based approach; hence, it does not make any assumption on the channel conditions and does not require any a priori information about the WSN (e.g., number of nodes). This makes it suitable for real-life scenarios in which operating conditions may change over time. JIT-LEAP allows nodes to derive the optimal setting autonomously, that is, by relying only on local measurements. Furthermore, it avoids unnecessary energy waste and, by learning from past history, is able to speed up the selection of the optimal setting. Following an active approach for adaptive algorithms,

3 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:3 JIT-LEAP relies on a change detection test to monitor network conditions and trigger the adaptation mechanism only when necessary [Boracchi and Roveri 2014]. In addition, a theoretically grounded statistical technique is considered to characterize the operating conditions of a network once a change has been detected (this is fundamental to identifying previously encountered network conditions). In summary, this article makes the following contributions. We propose a just-in-time adaptive algorithm for the CSMA/CA parameter setting in WSNs that is practical and suitable for real-life scenarios. To the best of our knowledge, JIT-LEAP is the first solution combining a statistical change detection test and a learning mechanism to promptly detect changes in the operating conditions and speed up the adaptation. We show, by simulation, that JIT-LEAP outperforms all the previous solutions meant to identify the optimal CSMA/CA setting in WSNs. The rest of the article is organized as follows. Section 2 presents related work. Section 3 describes the standard. Section 4 formulates the problem addressed in this article in a formal way. Section 5 presents the JIT-LEAP algorithm. Section 6 describes the simulation setup, while Section 7 presents the simulation results. Conclusions are drawn in Section RELATED WORK IEEE WSNs (in BE mode) have been extensively studied in the past; many proposals have been presented to improve their performance and/or introduce additional features not provided by the standard. A thorough review of the main proposed solutions is available in Khanafer et al. [2014], in which a taxonomy is also provided, based on eight different categories: Priority-based, QoS-based, Hidden Node Resolutionbased, IEEE based, Duty Cycle-based, Backoff-based, Parameter Tuning-based and Cross-Layer based. Priority-based and QoS-based solutions aim at adding functionalities and flexibility to the IEEE MAC protocol in order to provide better support to time-sensitive applications. This can be achieved by allowing priorities among sensor nodes [Kim and Kang 2010] or enhancing the GTS mechanism (see Section 3) [Na et al. 2008]. On a similar basis, Hidden Node Resolution-based approaches [Koubaa et al. 2009; Sheu et al. 2009] enhance the MAC protocol to make it more aware of the existence of hidden nodes. This reduces the number of collisions and allows better utilization of communication and energy resources. All the solutions belonging to the previous classes typically introduce modifications in the standard MAC protocol. IEEE based approaches [Lee et al. 2009] apply strategies conceived for improving the performance of Wireless LANs to WSNs. The main drawback of these solutions is that they have not been designed considering energy efficiency as a primary concern. Hence, they are not suitable for most WSNs. Duty-cycle based approaches [Kwon and Chae 2006; Lee et al. 2007; Neugebauer et al. 2005] dynamically adapt the duty cycle of sensor nodes to traffic conditions. Increasing the duty cycle gives sensor nodes more chances to transmit and, hence, reduces the contention for channel access. However, such solutions are ineffective when a large number of sensor nodes is transmitting simultaneously (e.g., periodic or eventdriven traffic). Furthermore, energy consumption increases with the duty cycle. Backoff-based approaches [Lee et al. 2009; Khan et al. 2010; Khanafer et al. 2011] propose modifications to the backoff algorithm of CSMA/CA. Basically, they adapt the backoff window size depending on network congestion and wireless medium conditions. The proposed modifications can actually increase the throughput and reduce the delay. However, they are not standard-compliant; hence, they cannot be adopted by sensor platforms implementing the MAC-layer functionalities in hardware or not allowing changes to the MAC protocol.

4 27:4 S. Brienza et al. Finally, Parameter Tuning-based [Zhao et al. 2010; Rao and Marandin 2006; Park et al. 2009; Park et al. 2013] and Cross-Layer based [DiFrancesco et al. 2011; Brienza et al. 2013a] solutions improve the performance/reliability of WSNs by appropriately tuning the CSMA/CA parameters. The difference between the two categories is that, in Cross-Layer based solutions, CSMA/CA parameters (i.e., MAC-layer parameters) are tuned by also exploiting information provided by other layers in the protocol stack (e.g., application, or network layer). Since both classes rely on the same basic idea (i.e., parameter tuning), for simplicity, hereafter we will refer to them generically as solutions based on parameter tuning. Such solutions do not modify the MAC protocol; hence, they can be implemented on any sensor platform. JIT-LEAP belongs to this category. The idea of tuning CSMA/CA parameters is motivated by a number of studies [Yedavalli and Krishnamachari 2008; Singh et al. 2008; Pollin et al. 2008; Anastasi et al. 2011] showing that the MAC has severe limitations in terms of reliability and timeliness, mainly due to an improper setting of its CSMA/CA algorithm. Specifically, Anastasi et al. [2011] have shown that unreliability in WSNs is exacerbated by the default CSMA/CA parameter values suggested by the standard, that are inappropriate, even when the number of sensor nodes is low. Using more appropriate (i.e., higher) parameter values improves reliability at the cost of increased latency and energy consumption. Solutions based on parameter tuning can be further distinguished, depending on the number of CSMA/CA parameters that they consider and the methodology that they use for their tuning. Some solutions [Zhao et al. 2010; Rao and Marandin 2006] focus on a single CSMA/CA parameter (e.g., macminbe). However, adjusting a single parameter may not be sufficient to meet the reliability requirements of the application [Anastasi et al. 2011]. For this reason, other solutions [Park et al. 2009; Park et al. 2013; DiFrancesco et al. 2011; Brienza et al. 2013a] consider the whole set of CSMA/CA parameters. JIT-LEAP also falls in the latter category; hence, hereafter, we will focus on such solutions. Regarding the methodology used for parameter tuning, according to the taxonomy introduced in Brienza et al. [2013b], the proposed solutions can be classified as model-based offline computation [Park et al. 2009], model-based adaptation [Park et al. 2013], and measurements-based adaptation [DiFrancesco et al. 2011; Brienza et al. 2013a]. Model-based strategies rely on an analytical model of the WSN to derive the optimal parameter setting under the current operating conditions. This is done either by solving the analytical model offline [Park et al. 2009] or by using it to dynamically adapt to timevarying operating conditions [Park et al. 2013]. Model-based approaches have a number of limitations. First, the effectiveness in providing the optimal setting depends on the accuracy of the analytical model. Typically, simplifying assumptions are introduced to make the model tractable. Furthermore, the model usually requires some input parameters, which may not be available in a real environment. For instance, the model used in Park et al. [2009] and Park et al. [2013] assumes ideal channel conditions and requires knowing in advance the number of network nodes. In contrast, JIT-LEAP considers a real communication channel in which packet errors/losses can occur, and does not require any input parameter. Hence, it is suitable for real-life scenarios. Measurement-based approaches [DiFrancesco et al. 2011; Brienza et al. 2013a] do not require any network model; instead, they rely on measurements acquired by sensor nodes. For instance, ADAPT [DiFrancesco et al. 2011] is a heuristic algorithm that allows sensor nodes to autonomously adjust the CSMA/CA parameters according to local measurements of the packet delivery probability. Specifically, parameter values are increased or decreased depending on the delivery probability experienced by the node. However, ADAPT tends to oscillate between two or more parameter sets and never

5 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:5 Fig. 1. Superframe structure. stabilizes, thus consuming more energy than necessary. Furthermore, it is memoryless. This means that, if the same operating conditions repeat over time, the algorithm is not able to recall the previously calculated optimal parameter setting and re-executes the adaptation procedure. Like ADAPT, JIT-LEAP follows a measurement-based approach, though the analyzed quantities are different. In addition, it also exploits the knowledge acquired through a learning mechanism to select the optimal parameter setting based on the past history. JIT-LEAP belongs to the class of active adaptive algorithms [Alippi 2014] since it relies on a trigger mechanism to activate the adaptation phase only when needed. In contrast to passive algorithms (e.g., Park et al. [2013]), in which the adaptation mechanism is always on, active algorithms are generally faster in adapting to new conditions, providing better performance and lower energy consumption. Formally, ADAPT is an active algorithm, as the adaptation mechanism is activated only when the locally estimated packet delivery probability is below/over a predefined threshold. In practice, ADAPT tends to change the parameter setting at (almost) every step, thus behaving similarly to passive algorithms. The JIT-LEAP algorithm presented in this article extends a previous LEarning-based Adaptive Parameter (LEAP) tuning algorithm presented in Brienza et al. [2013a]. While LEAP assumes ideal channel conditions (i.e., error/loss free channel), JIT-LEAP overcomes this limitation by explicitly taking into account packet losses and transmission errors. This makes it suitable for real-life scenarios. In addition, unlike LEAP, JIT- LEAP relies on a theoretically grounded mechanism to detect changes in the operating conditions, based on a statistical Change Detection Test (CDT). This allows significant reduction of the number of false-positive detections and the identification of even small variations in the operating conditions. Hence, the parameter setting provided by JIT-LEAP is more stable and accurate, allowing strict adherence to the application requirements MAC PROTOCOL The MAC in BE mode provides a power-management mechanism, based on a duty cycle, and relies on a superframe structure bounded by Beacons, that is, special messages transmitted periodically by coordinator nodes (Figure 1). The time interval between two consecutive Beacons is called the Beacon Interval (BI), and each superframe consists of an Active Period and an Inactive Period. During the Active Period, sensor nodes can communicate with their coordinator. In the Inactive Period, they enter a low-power state to save energy. The Active Period is further divided into a Contention Access Period (CAP) and a Collision Free Period (CFP). During the CAP, nodes use a slotted CSMA/CA algorithm for channel access; during the CFP, they use Guaranteed Time Slots (GTSs) in a Time Division Multiple Access (TDMA) style.

6 27:6 S. Brienza et al. Fig slotted CSMA/CA algorithm CSMA/CA Algorithm In the slotted CSMA/CA algorithm, used during CAP, time is divided into slots of equal duration (backoff slots) and all the operations are aligned with them. Upon receiving a data packet to transmit, each node executes a backoff stage, that is, it waits for a random number of backoff slots (backoff time), then performs two consecutive Clear Channel Assessments (CCAs) to check the channel state. If the channel is found idle in both CCAs, the node transmits its packet. Otherwise, it must perform a new backoff stage. After the transmission of a packet, the sensor node waits for the acknowledgment from the recipient. If the acknowledgment is not received within a predefined timeout, a retransmission is triggered. The transmission of a packet may result either in a success (if an acknowledgment is eventually received) or in a packet drop. A packet is dropped when either the maximum number of consecutive backoff stages or the maximum number of retransmissions is exceeded. Figure 2 presents the slotted CSMA-CA algorithm by detailing the sequence of actions performed by a sensor node to transmit a packet. Each node maintains a number of state variables: contention window size (CW), number of backoff stages (NB), backoff exponent (BE) and number of retransmissions (NR). CW specifies the number of CCAs still to perform in the current backoff stage. It is initialized to 2; hence, the sensor node

7 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:7 Table I. CSMA/CA Parameters and Values [IEEE ] PARAMETER VALUES DESCRIPTION MACMAXFRAMERETRIES Range: 0-7 Default: 3 MACMAXCSMABACKOFFS Range: 0 5 Default: 4 MACMAXBE Range: 3 8 Default: 5 MACMINBE Range: 0 7 Default: 3 Maximum number of retransmissions Maximum number of backoff stages 1 Maximum backoff window exponent Minimum backoff window exponent has to perform two consecutive CCAs before starting the packet transmission. BOE defines the maximum (random) backoff delay a node will wait at each backoff stage before checking the channel state. It is initialized to macminbe and incremented every time the channel is found busy during the CCAs, that is, before starting a new backoff stage (however BE cannot exceed macmaxbe). Basically, the number of backoff slots to wait in a backoff stage is randomly chosen in the interval [0; 2 BE 1]. NB indicates the number of backoff stages performed for the current transmission attempt. If NB exceeds the maximum allowed value macmaxcsmabackoffs, the packet is dropped. Finally, NR indicates the number of retransmissions for the current packet and is incremented every time the acknowledgement is not received. If NR exceeds the macmaxframeretries parameter, the packet is dropped. From the previous description, it emerges that the CSMA/CA behavior is regulated by four parameters, listed in Table I, together with the range of values allowed by the standard. DiFrancesco et al. [2011] show that, in a star topology, the packet delivery probability provided by CSMA/CA increases monotonically with the values of macminbe, macmaxcsmabackoffs, and macmaxframeretries. However, its increase becomes negligible after certain values of the aforementioned parameters. They also show that increasing macminbe is more energy efficient than increasing macmaxcsmabackoffs (i.e., it improves the packet delivery probability with a lower energy consumption), whereas increasing macmaxcsmabackoffs is more energy efficient than increasing macmaxframeretries. These conclusions are at the basis of the design of the JIT-LEAP algorithm (as described in Section 5). 4. PROBLEM FORMULATION In the following, we refer to a WSN with a star topology, including a sink node (acting as the coordinator) and a number of sensor nodes. We consider a periodic reporting application in which data gathered by a sensor node are reported to the sink at each BI. We assume that data/acknowledgment packets transmitted by nodes may be corrupted or lost. Despite that, the application requires a certain reliability level (expressed as percentage of data packets correctly delivered to the sink), that must be guaranteed with minimum energy consumption. To formulate the problem in a more formal way, we define the following indexes: Packet delivery ratio (D): the ratio between the number of data packets correctly delivered to the sink by a sensor node and the total number of packets generated by that node. It measures the long-term reliability experienced by a sensor node, and is requested to be higher than a minimum value D min. Miss ratio (M): the fraction of times that the packet delivery ratio calculated by a sensor node over the current BI drops below D min. It measures the inability to achieve short-term reliability and should not exceed a predefined threshold M max.

8 27:8 S. Brienza et al. Average energy consumption per packet (E P ): the total energy consumed by a sensor node divided by the total number of packets generated by that node. It measures the energy efficiency. Let D(par), M(par), and E P (par) denote the delivery ratio, miss ratio, and average energy consumption, respectively, experienced by a sensor node when using a set of CSMA/CA parameter values denoted by par. Hence, the problem of optimal parameter setting can be formulated as minimizee P (par) D (par) D min. (1) M (par) M max A possible approach for solving this problem is through the derivation of an analytical model of the WSN and the computation of the optimal CSMA/CA parameter setting that satisfy Equation (1). This is very close to the approach used in Park et al. [2009], in which the authors consider delivery ratio and latency (instead of miss ratio). As emphasized in Section 2, the use of a model-based approach has some limitations that make it unsuitable for real-life scenarios. In this article, we use a heuristic solution, following a measurement-based approach that leverages a change-detection test and a learning algorithm to identify the optimal setting adaptively. 5. JIT-LEAP ALGORITHM DESCRIPTION In this section, we describe the proposed JIT-LEAP algorithm. We start with a highlevel presentation (Section 5.1). Then, we detail the different phases of the algorithm (Sections 5.2 through 5.5). Finally, we describe some optimization mechanisms for improving its energy efficiency (Section 5.6) Basic Ideas The goal of JIT-LEAP is to select the set of CSMA/CA parameter values (depending on the current operating conditions) that satisfy the reliability requirements of the application with minimum energy consumption at sensor nodes. To this end, it also exploits the knowledge learned from past history (if any). Figure 3 details the actions performed by JIT-LEAP during each BI. First, each node characterizes the current network conditions by measuring some quantities related to network congestion and channel unreliability (see Section 5.2). In addition, each node derives the estimates of delivery ratio and miss ratio experienced in the current BI and inserts them into a specific data structure called Experienced-Performance Table (see Sections 5.2 and 5.3). The latter table is used to store the performance experienced, with each set of parameters, since the last change in the network conditions. Then, the algorithm behaves in different ways depending on its current operating phase, namely, Adaptive Tuning or Change Detection Phase. 1) Adaptive Tuning Phase (right side of Figure 3). When no information about the current operating conditions is available (e.g., at startup), the sensor node executes an Adaptive Tuning algorithm similar to ADAPT [DiFrancesco et al. 2011]. CSMA/CA parameter values increase when the reliability experienced by the sensor node (in terms of D and M) does not satisfy the application requirements, and decrease otherwise. After a number of steps, the Adaptive Tuning algorithm starts oscillating between two parameter sets. This means that the most appropriate setting for the current conditions has been reached. Hence, this information is inserted into an appropriate data structure, called Learning Table (details to follow) which indicates, for each parameter set, the optimal set to be used if a certain network condition is encountered. Then, the algorithm moves to the Change Detection Phase.

9 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:9 Fig. 3. Actions performed by JIT-LEAP during each Beacon Interval. 2) Change Detection Phase (left side of Figure 3). This phase aims at detecting possible changes in the operating conditions, to trigger the adaptation to the new conditions. To this end, a Change Detection Test (CDT), that is, an online statistical test, is performed to detect possible variations in the operating conditions measuring network congestion and channel unreliability. If no change is detected, the current CSMA/CA parameter values used by the sensor node are not updated and no further actions are performed. Conversely, if a change is detected, JIT-LEAP first identifies the new operating conditions, then determines the new optimal setting. If similar conditions have already been experienced in the past, the learning mechanism allows immediate reactivation of the optimal setting previously used. Specifically, upon detecting a change, the algorithm checks if there is an entry in the Learning Table corresponding to the current set and the new network conditions. The following two outcomes can occur. The Learning Table contains an entry matching the new operating conditions with the corresponding optimal setting. Therefore, the node sets up the optimal parameter values suggested by the table (in just one step, or leap). Afterwards, the Change Detection phase restarts. There is no entry in the Learning Table for the new operating conditions. Therefore, a new Adaptive Tuning phase starts. In the next sections, we will detail the data structures used by JIT-LEAP and the actions carried out during the Adaptive Tuning and Change Detection phases State Assessment and Data Structures We use s(t) = [p b (t), p f (t), par(t)] to store the state of the sensor network, as perceived by a generic sensor node, at a given BI t. Specifically, par(t) is the used set of CSMA/CA parameter values, p b (t) denotes the probability of finding the channel busy during a channel access, and p f (t) gives the probability that a packet transmission fails (i.e.,

10 27:10 S. Brienza et al. the sensor node does not receive the related acknowledgment). In particular, p b is a measure of the congestion experienced by the sensor node and depends on factors such as number of sensor nodes and offered load. It also depends on the CSMA/CA parameter setting used by the sensor node, that is, par. On the contrary, p f measures communication unreliability and mainly depends on wireless medium unreliability (i.e., the Packet Error Rate, PER). However, it also depends on network congestion, since a transmission can fail due to a collision. Despite p b and p f depending on many different factors, for simplicity, we will use the terms p b (t) and p f (t) to indicate their values at BI t. The state vector s(t) is derived by the sensor node as follows. The CSMA/CA parameter values (i.e., par(t)) are known. p b (t) can be measured locally as p b (t) = pb 1 + ( 1 pb) 1 p 2 b, where pb 1 (p2 b ) is the probability of finding the channel busy during the first (second) CCA operation. In practice, pb 1 and p2 b are estimated by calculating the fraction of CCA operations resulting in a busy channel in the current BI. Similarly, p f (t) is computed as the fraction of transmissions for which the acknowledgment was missed during the current BI. At each sensor node, JIT-LEAP uses the following data structures to store information. Experienced-Performance Table. A table with an entry for each CSMA/CA parameter setting used since the last change in the operating conditions (or network startup). The table is cleared whenever a new change is detected. Each entry has the following format: par, D, M, F, count, where D (M) represents the delivery ratio (miss ratio) experienced by the sensor node with the par parameter set. F denotes the Transmission Failure Ratio, defined as the ratio between the number of transmissions for which the acknowledgment was missed and the total number of transmissions performed by the sensor node using the par parameter set. Finally, count indicates the number of times the corresponding parameter set has been used so far. Training Buffer. A data structure containing the last W experienced states. It is needed for training the CDT, both at network startup and after a change detection. State Sample. Whenever the CDT detects a change in the operating conditions, it estimates the BI τ when the change more likely occurred. Then, it calculates the mean value and standard deviation of p b and p f over the BIs between τ and the instant when the change has been detected. These values characterize the new operating conditions. Thus, they are inserted into a proper data structure, called State Sample, that will be used to build the Learning Table at the end of the next Adaptive Tuning phase. Learning Table. This data structure is created at the end of the first Adaptive Tuning phase and updated after each Adaptive Tuning phase on the basis of the State Sample. The Learning Table contains information about each operating condition experienced during the past history, and the corresponding optimal setting, according to the previously acquired knowledge. Each entry in the table has the following format: par,elem 1,elem 2,...,elem i,..., where elem i = [ pb i min, pi b max],[p i f min, p i f max ], new_set for any i. Basically, each operating condition is represented by an element elem, where the two intervals [p b min,p b max ]and[p f min,p f max ] indicate the range of p b and p f characterizing that specific operating condition. Therefore, the table tells that, whenever the estimated values of p b and p f fall within the previously mentioned intervals, and the parameter set par is used, the new optimal setting must be new_set. Examples on how to access and use the Learning Table are given later Experienced-Performance Table Update As anticipated in Section 5.1, CSMA/CA parameter values are increased or decreased depending on the current estimates of delivery ratio and miss ratio (i.e., D and M). For

11 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:11 this reason, for each used set, the algorithm stores, inside the Experienced-Performance Table, the value of D and M experienced with that set. At each BI, the entry corresponding to the current set is updated, as follows: D = D + D count count + 1 M = M + M count. count + 1 D and M represent the delivery ratio and miss ratio measured in the current BI, while count tracks the number of times the corresponding set has been used so far (it is increased after each update). This way, the estimates of D and M are increasingly more accurate over time. If the channel is ideal (i.e., PER = 0), D can be obtained as D = PAC K /P gen, where P gen is the number of packets generated by the sensor node and P AC K is the number of received acknowledgments. Furthermore, if D > D min,then M = 0; otherwise M = 1. If the channel is not ideal (i.e., PER > 0), the previous formula for D underestimates the delivery ratio, since a packet may have been delivered correctly to the sink even if the corresponding acknowledgment was missed by the sensor node. To correctly estimate the delivery ratio, when PER > 0, we also need to take into account the packets dropped due to exceeded number of retransmissions, but correctly received by the sink. Let P MFR denote the total number of packets dropped due to exceeded number of retransmissions and ± be the probability that a dropped packet is received correctly by the sink. The delivery ratio can be estimated as D = P AC K+P MFR α P gen. The value of P MFR is provided by the MAC layer, while ± can be derived using the following claim. CLAIM 1. Assuming that (i) packet transmission errors are independent from each other, and (ii) the PER is the same for both data packets and acknowledgments, then ( ) F PER macmaxframeretries+1 α = 1, (1 PER)F where F denotes the transmission failure ratio, that is, the probability that a packet transmission fails for any reason. PROOF. See Appendix A. The previous claim allows derivation of α, onceper and F are known. PER is estimated by the sensor node by computing the ratio between the number of missed Beacons and the number of expected Beacons. Instead, the transmission failure ratio F is estimated by taking an approach similar to that used for estimating D. As mentioned earlier, for each used parameter set, the corresponding entry in the Experienced-Performance Table also includes a field F. The latter is updated, at each BI, as F = F+F count count+1, where F is the ratio between the number of missed acknowledgments and the total number of transmissions (including retransmissions) performed by the sensor node in the current BI Adaptive Tuning Phase CSMA/CA Parameters Change. As shown in Figure 3, initially, JIT-LEAP starts with a simple Adaptive Tuning algorithm to dynamically adjust CSMA/CA parameters, as it has no information about the past history. This algorithm increases or decreases one parameter at a time, depending on the experienced reliability, as follows. At each BI, the sensor node updates the estimates of delivery ratio D and miss ratio M with measurements taken in the current BI. If at least one of these estimates does not satisfy the application requirements, the value of a CSMA/CA parameter is increased by considering, first, macminbe, then, macmaxcsmabackoffs (macmaxbe is kept to a

12 27:12 S. Brienza et al. Table II. Ordered CSMA Parameter Sets INDEX MAXBE MINBE MAXCSMABACKOFFS MAXFRAMERETRIES 1 MAXBE MAX MINBE MIN MAXCSMABACKOFFS MIN MAXFRAMERETRIES MIN 2 MAXBE MAX MINBE MIN +1 MAXCSMABACKOFFS MIN MAXFRAMERETRIES MIN 3 MAXBE MAX MINBE MIN +2 MAXCSMABACKOFFS MIN MAXFRAMERETRIES MIN MAXBE MAX MINBE MAX MAXCSMABACKOFFS MIN MAXFRAMERETRIES MIN... MAXBE MAX MINBE MAX MAXCSMABACKOFFS MIN +1 MAXFRAMERETRIES MIN... MAXBE MAX MINBE MAX MAXCSMABACKOFFS MIN +2 MAXFRAMERETRIES MIN MAXBE MAX MINBE MAX MAXCSMABACKOFFS MAX MAXFRAMERETRIES MIN... MAXBE MAX MINBE MAX MAXCSMABACKOFFS MAX MAXFRAMERETRIES MIN MAXBE MAX MINBE MAX MAXCSMABACKOFFS MAX MAXFRAMERETRIES MIN I MAX MAXBE MAX MINBE MAX MAXCSMABACKOFFS MAX MAXFRAMERETRIES MAX fixed value, i.e., MaxBE max ). The retransmission mechanism is initially disabled. Only when both macminbe and macmaxcsmabackoffs have reached their maximum value, macmaxframeretries is also progressively increased. Conversely, if both D and M satisfy the application requirements, the set of parameter values is tentatively reduced. The strategy for decreasing parameters is the opposite. First, macmaxframeretries is progressively reduced until it reaches its minimum value. Then, the same procedure is applied to macmaxcsmabackoffs and, afterwards, to macminbe. Without loss in generality, we can assume that CSMA/CA parameter sets are ordered as shown in Table II. Hence, each parameter setting can be identified by the corresponding index in the table and the Adaptive Tuning algorithm always moves from a set to an adjacent one Training Buffer and Learning Table Update. The Training Buffer and Learning Table are also updated during the Adaptive Tuning phase. At each BI t, after estimating p b (t) and p f (t), the new state s(t) = [p b (t), p f (t), par (t)] is added to the Training Buffer. Since the Training Buffer has a limited size, when it is full, the new state overwrites the oldest one, following a FIFO approach. We emphasize that, due to its behavior, the Adaptive Tuning algorithm tends to oscillate between two adjacent parameter sets after a (short) transient time. We assume that the Adaptive Tuning phase ends when all the states stored inside the Training Buffer refer to only two parameter sets. Then, the Training Buffer is ready to be used for training the CDT, as described later. The most frequent setting within the Training Buffer is assumed to be the most appropriate set for the current operating conditions, that is, the optimal set according to the Adaptive Tuning algorithm. Throughout, we will refer to this set as par opt. Now, a new element can be added in the Learning Table, pointing to the optimal set par opt. Let us denote by par prev the parameter set used before the current Adaptive Tuning phase started, that is, before the operating conditions changed. Also, let us indicate as μ b (μ f )andσ b (σ f ) the mean value and standard deviation of p b (p f ) inserted by the CDT into the State Sample. As explained in Section 5.2, these values have been calculated after the change occurred but before the Adaptive Tuning phase started. Hence, they characterize the new operating conditions. Therefore, a new entry corresponding to set-index par prev can be inserted into the Learning Table (if there is no entry for this set, a new entry is created). The added element is [μ b σ b,μ b + σ b ], [μ f σ f,μ f + σ f ], par opt

13 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:13 In the future, if these operating conditions are encountered again, while the set par prev is used, the algorithm immediately knows that the set par opt hastobeused. The update of the Learning Table concludes the Adaptive Tuning phase. Then, the sensor node enters the Change Detection phase Change Detection Phase Change Detection Test. JIT-LEAP detects possible changes in the operating conditions by inspecting variations in p b and p f. To achieve this goal, among the wide range of CDTs available in the literature [Basseville et al. 1993; Tartakovsky et al. 2006; Ross et al. 2011; Alippi and Roveri 2008; Kawahara and Sugiyama 2012], we focus on the family of CDTs based on the Intersection-of-Confidence-Interval (ICI) rule [Alippi et al. 2011], which is revealed to be particularly effective in several application scenarios [Alippi et al. 2013; Boracchi et al. 2014]. In addition, ICI-based CDTs are theoretically grounded and exhibit a reduced computational complexity, which makes them particularly suitable for WSNs. Finally, this family of CDTs follows the nonparametric approach, that is, they do not require any a priori information about the measured state variables or changes that might affect the network. This makes ICI-based CDTs particularly suitable for time-varying and a priori unknown environments (such as WSNs). Among the ICI-based CDTs, we focus on the element-wise CDT [Boracchi and Roveri 2014]. This CDT is able to operate in an element-wise manner, thanks to a Gaussian transform of measured variables, providing very prompt detections to changes. The considered Gaussian transform is the Manly transform: e λpi(t) 1 ; λ 0 p i (t) = λ, p i (t) ; λ = 0 where p i (t) can be either p b (t) or p f (t) and λ R is the transform parameter. The Manly transform is applied both to p b (t) and p f (t) to generate the approximately Gaussian variables p b (t) and p f (t). As mentioned earlier, this CDT requires an initial training sequence to configure the test parameters and the parameter λ of the Manly transform. Specifically, in our scenario, the CDT is configured on the Training Buffer. Details about the configuration phase of the CDT can be found in Boracchi and Roveri [2014]. During the operational life, the CDT is then applied to p b (t) and p f (t) to detect possible variations in their expected values, based on what has been learned during the training phase. When a change is detected, the Learning Table is looked up to determine the optimal set for the new operating conditions. A key requirement for obtaining correct values from the Learning Table is the ability to correctly characterize the operating conditions after the change, in terms of the new values of p b and p f. To achieve this goal, once a change is detected, it is necessary to determine when it occurred. Therefore, a Change- Point Method (CPM) is applied to the Training Buffer containing the last W acquired data to identify the time instant at which the operating conditions changed. CPMs are statistical hypothesis tests [Hawkins et al. 2003] that are able to assess whether a change point exists in a given sequence of data and to locate it within the sequence. Specifically, let ˆT be the BI when the change was detected (either in p b or p f ), and let X be the sequence of the corresponding variable up to ˆT,thatis: X ={ p D (( ˆT W + 1)),..., p D ( ˆT )},

14 27:14 S. Brienza et al. Table III. Example of Learning Table ELEM1 ELEM2 CURRENT SET p b p f new set p b p f new set par1 [0.30, 0.33] [0.33, 0.52] par2 [0.64, 0.70] [0.29, 0.51] par3 par2 [0.43, 0.51] [0, 0.24] par3 par3 [0.70, 0.75] [0.16, 0.22] par5 par4 [0.64, 0.76] [0.20, 0.43] par8 [0.25, 0.35] [0, 0.15] par1 where p D (t) iseitherp b or p f. The CPM acts as follows. For each BI t, such that ˆT W + 1 t ˆT, the sequence X is split into two parts: A t ={ p D ( ˆT W + 1),..., p D (t)} B t ={ p D (t + 1),..., p D ( ˆT, )} and a test statistics (T t = A t, B t ) is computed for all the BIs t with ˆT W + 1 t ˆT. Let T M be its maximum value, that is: T M = max t= ˆT W+1,...,T T t. When T M is larger than a predefined threshold H ε, ˆT (that depends on the test statistic, ˆT and a given confidence level ε), there is enough statistical confidence that a change point exists in X.Letτ be the time instant of this change point, that is: τ = argmax T t. t= ˆT W+1,...,T Among the test statistics present in the literature (e.g., Mann and Whitney [1947], Bartlett and Kendall [1946], Mood [1954], and Lepage [1974]), we focused on Mann and Whitney [1947] since we are interested in detecting change points affecting the expected value of X. We emphasize that τ represents an estimate of the BI at which a change affected the operating conditions. Hence, the new operating conditions can be computed as follows: μ = 1 ˆT τ σ = ˆT i=τ 1 ˆT τ 1 p D (i) ˆT i=τ ( p D (i) P D ) 2, where μ and σ are the sample mean and sample variance, respectively, of the state variable p D (t) after the change occurred. The values of μ and σ, for both p b and p f (μ b, σ b, μ f and σ f ), represent the new operating conditions and are stored inside the State Sample Learning Table Access. Once a change has been detected, the Learning Table is checked to verify whether the new conditions have been experienced in the past already. To this aim, the current set index are used, along with the values of μ b and μ f contained in the State Sample. Table III shows an example of a Learning Table. Let us assume that par4 is the current parameter set and that ˆμ b and ˆμ f are the values of μ b and μ f stored in the State Sample. Based on the past history, the Learning Table suggests to use par8 as the new set, if ˆμ b is in the range [0.64, 0.76] and ˆμ f is in the range [0.20, 0.43], or par1, if ˆμ b is in the range [0.25, 0.35] and ˆμ f in the range [0, 0.15].

15 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:15 When the Learning Table does not contain any entry for the values in the State Sample, JIT-LEAP infers that the current operating conditions have never been experienced in the past, and a new Adaptive Tuning phase is started to identify the optimal MAC parameter set. When the optimal set is determined, at the end of the Adaptive Tuning phase, a new entry is added to the Learning Table by using the data contained in the State Sample, as previously explained Controlled Tuning Algorithm The Adaptive Tuning phase aims at identifying the parameter setting that satisfies the reliability requirements of the application with minimum energy consumption. However, since CSMA/CA parameters assume discrete values, typically, the delivery ratio (miss ratio) experienced with the obtained parameter set is significantly above (below) D min (M max ), thus consuming more energy than necessary. On the other hand, using a lower set might not satisfy the application requirements. To reduce energy consumption as much as possible while still satisfying the reliability constraints, JIT-LEAP uses a Controlled Tuning algorithm (during both the Adaptive Tuning phase and the Change Detection phase) that finely adjusts the parameter setting on the sensor node, by switching between two adjacent sets in a controlled way. The idea is to have a reliability level just above the required value to minimize energy consumption. The Controlled Tuning algorithm is detailed in Appendix B. 6. SIMULATION SETUP To evaluate the performance of JIT-LEAP, we relied on the ns2 simulation tool [Ns ]. We used simulation in order to make the analysis as general as possible. However, to validate our simulation results, we also implemented JIT-LEAP in a real sensor platform and carried out some experiments in a real testbed. The comparison between simulation and experimental results is shown in Appendix C (due to space limitations). We considered a star network topology, in which sensor nodes are placed in a circle centered at the sink node (PAN coordinator), 10m away from it. The transmission range was set to 15m, while the carrier sensing range was set to 30m (according to Anastasi et al. [2005]). In our analysis, in addition to the reliability and energy efficiency indexes already introduced in Section 4 (i.e., packet delivery ratio, miss ratio, and average energy consumption per packet), we also considered the following two performance indexes. Average latency, defined as the average time from the beginning of the packet transmission at the source node to when the packet is correctly received by the sink. This index measures the timeliness in delivering packets. Transient time, defined as the time instant, after a change in the operating conditions, when the packet delivery probability calculated over the current BI reaches the steady-state value for the new operating conditions (with a tolerance of ±3%). This index measures the ability to adapt to changing conditions. The energy consumed by a sensor node is calculated according to the model in Bougard et al. [2008], which is based on the Chipcon CC2420 radio transceiver [Texas Instruments 2012] commonly used in sensor nodes Algorithms for Comparison We compared the performance of JIT-LEAP with that of the following algorithms. Model-based offline computation [Park et al. 2009]. This algorithm derives the optimal setting offline by solving an analytical model of the WSN. The algorithm is

16 27:16 S. Brienza et al. Table IV. Operating Parameters PARAMETER VALUE Bit Rate 250Kbps Dataframe (payload) size 109 (100)B ACK frame size 11B Beacon Order (BO), Superframe Order (SO) 13, 8 MinBE min, MinBE max 1, 7 MaxBE max 10 MaxCSMABackoffs min, MaxCSMABackoff max 1, 10 MaxFrameRetries min, MaxFrameRetries max 0, 3 Power consumption mW, 52.2mW, in RX, TX, idle, sleep mode 1.28mW, 0.06mW Training Buffer size (W) 15 executed on the sink node and parameter values are then communicated to sensor nodes. Model-based online adaptation [Park et al. 2013]. This is an adaptive algorithm based on an analytical model of the WSN, which is a simplified version of that used in the previous algorithm, hence can be executed at sensor nodes. Sensor nodes measure some congestion indexes locally and use them as input values for the model to adapt the CSMA/CA parameter values to time-varying operating conditions. ADAPT [DiFrancesco et al. 2011]. ADAPT is a measurement-based heuristic algorithm that dynamically increases/decreases the CSMA/CA parameter values one at a time in such a way that the measured delivery ratio remains confined within a region defined by two thresholds D low and D high and above the minimum value D min required by the application. ADAPT also includes a control mechanism to achieve the required reliability in the case of an unreliable channel. Each sensor node measures the experienced packet error/loss rate and enables retransmissions if the measured value exceeds a predefined threshold D loss. LEAP [Brienza et al. 2013a]. This is the preliminary version of JIT-LEAP. It assumes ideal channel conditions and does not rely on a statistical CDT to detect changes Parameter Values and Methodology Table IV summarizes the operating parameters used in our simulations. Since all the other algorithms (except LEAP) do not consider miss ratio when deriving the optimal setting, the operating parameters for these algorithms have been chosen in such a way as to guarantee both D min and M max required by the application. This allows a fair comparison of the considered algorithms in terms of both energy consumption and latency. In our simulations, we considered both ideal and noisy channels. In the latter case, we used the Gilbert-Elliot (GE) model [Gilbert 1960; Elliot 1963] to simulate packet errors/losses, as it provides a good approximation of fading in real environments [Willig et al. 2002]. The channel is represented by a continuous-time Markov chain, consisting of two states: bad and good. In the bad state, no packet can be successfully delivered; in the good state, all packets are correctly received. Sojourn times in the two states follow an exponential distribution and their average value determines the average PER experienced during the entire simulation. To derive the model parameters, we took an approach similar to De Pellegrini et al. [2006] and Anastasi et al. [2011] and used values inspired from the real measurements in Willig et al. [2002]. It turns out that, when the PER is equal to 10%, the average sojourn time in the bad and good 1 Power consumptions have been derived from the CC2420 datasheet [Texas Instruments 2012], considering a voltage equal to 3V and a transmission power of 0dBm.

17 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:17 Fig. 4. Delivery ratio (left) and miss ratio (right) versus number of sensor nodes. state is 5.7ms and 46.2ms, respectively. Larger values of the PER are obtained by changing the average sojourn time in the bad state accordingly, while leaving all the other parameters unchanged. We also assumed that each sensor node generates 10 data packets at every BI. All these packets are simultaneously passed down to the MAC layer at the beginning of each BI. For each simulated scenario, we performed 10 independent replications, each consisting of 1000 BIs. For each replication, we discarded the initial transient interval (10% of the overall duration) during which nodes associate to the PAN coordinator and start generating packets. The results presented in the next section are averaged over all replications. We also derived confidence intervals using the independent replications method and 95% confidence level. In some cases, the confidence intervals are too small to be observed in the figures. 7. SIMULATION RESULTS Our analysis is divided into two parts. In the first part, we compare the considered algorithms in stationary conditions, that is, we assume that the operating conditions do not change over time. In the second part, we consider dynamic scenarios with timevarying operating conditions. Since the two model-based algorithms (and LEAP as well) assume ideal channel conditions, in our analysis both in stationary and dynamic scenarios we initially assume that packet errors/losses never occur (i.e., PER = 0). Then, we restrict our analysis to ADAPT and JIT-LEAP only, and investigate the impact of PER on their performance. In our simulations, we assumed that the application requires a packet delivery ratio D 80% and a miss ratio M 20%, for any sensor node (i.e., D min = 0.80 and D max = 0.20). Obviously, these thresholds are somehow arbitrary, as they strongly depend on the specific application. However, we performed additional simulations with different thresholds (omitted for space limitations), and we achieved results in line with those presented here Analysis in Stationary Conditions As mentioned earlier, we start our analysis in stationary conditions assuming an ideal channel. Figure 4 shows the delivery ratio and miss ratio of a generic sensor node, for an increasing size of the WSN. All the algorithms satisfy the reliability requirements, both in terms of D and M, with the only exception of LEAP, which exhibits a miss ratio slightly above M max. The offline algorithm provides the highest delivery ratio and the lowest miss ratio. However, it also exhibits the largest latency and energy consumption, as shown in Figure 5. ADAPT provides a delivery ratio between the two

18 27:18 S. Brienza et al. Fig. 5. nodes. Average per-packet energy consumption (left), and average latency (right) versus number of sensor thresholds, D low and D high, that have been determined to satisfy also the miss ratio constraint. The model-based adaptive algorithm and JIT-LEAP have similar performance in terms of delivery ratio and miss ratio. However, due to the Controlled Tuning algorithm, JIT-LEAP provides a delivery ratio (miss ratio) very close to D min (M max ). This allows JIT-LEAP to reduce the energy consumption, as shown in Figure 5 (left). We emphasize that JIT-LEAP is the best solution in terms of energy consumption. In terms of latency (Figure 5, right), the model-based adaptive algorithm has the best performance. This is because the latter algorithm tends to improve the delivery ratio by increasing the number of retransmissions (macmaxframeretries), whereas the other algorithms achieve the same result by increasing the number of backoff stages (macmaxcsmabackoffs). When a packet is retransmitted, the Backoff Exponent (BE) is reinitialized to its minimum value. Instead, when a new backoff stage is started, the BE is doubled (unless it has reached its maximum value). However, the lower latency introduced by the model-based adaptive algorithm is paid in terms of higher energy consumption. This is because increasing the number of retransmissions is more energy consuming than increasing the number of backoff stages [DiFrancesco et al. 2011]. Finally, JIT-LEAP performs significantly better than both ADAPT and the model-based offline algorithm, also in terms of latency. Figures 4 and 5 show that LEAP and JIT-LEAP exhibit a similar trend for all the performance indexes. However, LEAP exhibits a higher miss ratio and slightly exceeds the maximum value M max. This is because the mechanism used by LEAP to detect changes in the operating conditions results in more false positives than the CDT used by JIT-LEAP. In our simulations, we observed a percentage of wrong detections (vs. the total number of detections) less than 1% for JIT-LEAP and close to 7% for LEAP. This means that, even in stationary conditions, LEAP can erroneously detect changes, thus triggering unnecessary variations in the CSMA/CA parameter setting. Given the higher stability of JIT-LEAP and its accuracy in determining the best set of MAC parameter values, it is more suitable than LEAP for all those critical applications that require minimum guaranteed reliability levels. In the second set of simulations in stationary conditions, we consider a nonideal channel. Specifically, we consider different values for the average PER experienced over the simulation run. In this set of simulations, the number of sensor nodes is constant and equal to 30. As anticipated, this analysis does not consider both model-based algorithms and LEAP, since they assume ideal channel conditions. Therefore, the analysis is restricted to JIT-LEAP and ADAPT. The capacity of working under lossy channel conditions makes these two solutions much more convenient than the others, since they can be effectively used in real-life scenarios in which packet errors/losses occur

19 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:19 Fig. 6. Delivery ratio (left) and miss ratio (right) versus Packet Error Rate. Fig. 7. Average per-packet energy consumption (left), and average latency (right) versus Packet Error Rate. and PER changes over time. Indeed, Figure 6 shows that both JIT-LEAP and ADAPT satisfy the reliability requirements (in terms of D and M). However, JIT-LEAP outperforms ADAPT in terms of energy consumption and latency. The difference is mainly due to the way that the two algorithms estimate the delivery ratio experienced by a sensor node. Specifically, JIT-LEAP relies on a more effective mechanism (as explained in Section 5.3), since when an acknowledgment is missed it distinguishes between packet loss/corruption and acknowledgment loss/corruption. Conversely, ADAPT does not consider the effect of lost/corrupted acknowledgments; thus, it underestimates the delivery ratio experienced by the sensor node. Hence, it tends to use CSMA/CA parameter values higher than necessary, which result in higher energy consumption (up to 20%) and latency (see Figure 7) Analysis in Dynamic Conditions We now turn our attention to dynamic scenarios, in which operating conditions vary over time. We limit our analysis to adaptive algorithms, since the model-based offline algorithm is not suited for such scenarios. In the first set of simulations, we consider a scenario in which the number of active sensor nodes changes over time. We assume that 10 sensor nodes are always active, while 50 more nodes activate and deactivate simultaneously and periodically, every 300 BIs. Our goal is to investigate how the different algorithms react to such changes. The results presented here refer to nodes that are always active. Figure 8 shows the transient time taken by the various algorithms to adapt to the new operating conditions. We analyzed separately the transient originated by an increase and a decrease in the number of active nodes (left and right sides of Figure 8, respectively). As a general

20 27:20 S. Brienza et al. Fig. 8. Transient time when the number of active nodes increases (left) and decreases (right). remark, transient times experienced by JIT-LEAP and LEAP tend to become shorter and shorter as time elapses, while they remain approximately constant for the other algorithms. This is due to the learning mechanism used by JIT-LEAP and LEAP. When the WSN passes through similar operating conditions experienced in the past, they are able to find out the optimal setting by exploiting the information available in the Learning Table. Let us now focus on deactivation events (Figure 8, right). After a number of steps, JIT- LEAP and LEAP become significantly faster than the other two algorithms. In ADAPT, the transient time depends on the number of active sensor nodes, as the algorithm converges to the optimal setting step by step, and a larger network generally requires higher CSMA/CA parameter values to achieve the same reliability. The model-based adaptive algorithm converges in about 5 BIs as the optimal setting is derived by using samples measured in the previous m BIs (we used m = 4 in our simulations). However, both ADAPT and the model-based adaptive algorithm exhibits some drawbacks. The latter assumes to know in advance the number of (active) sensor nodes in the WSN. This is generally difficult to predict and may become a serious issue in dynamic scenarios. In our simulations, we ran the algorithm using the maximum number of sensor nodes (i.e., 60). This means that, when there are only 10 nodes, the provided setting is not optimal and sensor nodes consume more energy than necessary. Conversely, running the algorithm with the minimum number of nodes (i.e., 10) has negative drawbacks as well. When the number of active nodes is larger, the algorithm may not satisfy the reliability constraints required by the applications. Similarly, ADAPT requires the definition of the two thresholds D low and D high that strictly depend both on reliability requirements (M max and D min ) and network congestion. When the number of sensor nodes increases, the two thresholds should take larger values in order to guarantee the same levels of D and M. As outlined earlier, in our simulations, we referred to the worst case (60 active nodes) to define the threshold values to satisfy the reliability constraints both with 10 and 60 nodes. JIT-LEAP and LEAP do not suffer from such limitations, as they do not require any input parameter. This leads to significant benefits, especially in terms of energy consumption. Figure 9 compares the delivery ratio (left) and energy consumption (right) of the different algorithms before and after an increase in the number of sensor nodes has occurred. JIT-LEAP and LEAP are characterized by a delivery ratio that is the closest to the application requirement (80%), and provide the lowest energy consumption. This is because they use a more appropriate (i.e., lower) parameter setting than the other algorithms. For the same reason, when the number of sensor nodes changes abruptly, the parameter setting used by JIT-LEAP and LEAP is the least appropriate to the new conditions. Hence, they experience the biggest drop in the delivery ratio, as shown in Figure 9 (left).

21 Just-in-Time Adaptive Algorithm for Optimal Parameter Setting in WSNs 27:21 Fig. 9. Delivery ratio (left) and energy per packet (right) when the number of active nodes increases. Fig. 10. Transient time when the Packet Error Rate increases (left) and decreases (right). As a final remark, we need to point out that JIT-LEAP and LEAP exhibit similar performance under ideal channel conditions, both in terms of transient time and energy consumption. However, once again, the introduction of the CDT makes JIT-LEAP much more stable in the choice of parameter setting and, thus, more reliable. As shown in Figure 9 (left), in the interval 400 to 450, LEAP moves to a nonappropriate setting, thus temporarily violating the reliability requirements, due to some false positives in the detection of changes. Conversely, the problem does not occur with JIT-LEAP. In the second set of simulations, we consider a scenario in which the average PER changes over time during the simulation run (conversely, the number of sensor nodes is constant and equal to 30). Specifically, we assume that PER changes periodically (every 300 BIs) and abruptly, from 0% to 30% and vice versa. Similar to the analysis in stationary conditions with nonideal channels, this part of the analysis is limited to ADAPT and JIT-LEAP. As shown in Figure 10, ADAPT exhibits shorter transient times than JIT-LEAP. This difference can be explained as follows. In ADAPT, retransmissions are generally disabled (macmaxframeretries = 0) and are enabled only when a packet error/loss rate larger than D loss is experienced 2. When this occurs, macmaxframeretries is set to the maximum value allowed by ADAPT (i.e., 3). Obviously, such an approach makes ADAPT very reactive. However, since retransmissions are very energy consuming [DiFrancesco et al. 2011], this approach also introduces a larger energy consumption (see Figure 11, right). On the contrary, JIT-LEAP derives the exact value of macmaxframeretries in order to satisfy the reliability constraints required by the application. In addition, as explained earlier, ADAPT tends to underestimate the delivery ratio experienced by the sensor node, thus consuming more energy than necessary. For all these reasons, JIT-LEAP matches the application requirement 2 In our simulations we considered D loss = 1 ( D low + D hight) /2.